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Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
1

%I #8 Jan 25 2019 08:28:26

%S 5,25,125,612,2956,14125,66925,314935,1473779,6865098,31856590,

%T 147352985,679742085,3128486473,14370696813,65902020548,301787376436,

%U 1380297559417,6306497302225,28787967919963,131309246498679,598532215284482

%N Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

%H R. H. Hardin, <a href="/A269615/b269615.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 93*a(n-2) + 220*a(n-3) - 115*a(n-4) - 168*a(n-5) - 44*a(n-6) - 16*a(n-7).

%F Empirical g.f.: x*(5 - 55*x + 190*x^2 - 163*x^3 - 136*x^4 - 40*x^5 - 12*x^6) / ((1 - 4*x)*(1 - 12*x + 45*x^2 - 40*x^3 - 45*x^4 - 12*x^5 - 4*x^6)). - _Colin Barker_, Jan 25 2019

%e Some solutions for n=7:

%e ..3. .1. .0. .1. .4. .3. .4. .1. .1. .1. .1. .0. .2. .3. .2. .3

%e ..2. .4. .3. .1. .1. .3. .3. .0. .2. .2. .2. .1. .2. .0. .0. .4

%e ..0. .2. .1. .3. .2. .3. .2. .4. .0. .1. .3. .2. .3. .3. .2. .1

%e ..4. .4. .1. .4. .2. .4. .1. .4. .2. .2. .0. .1. .0. .3. .3. .0

%e ..0. .0. .1. .1. .2. .3. .1. .2. .1. .2. .4. .4. .1. .4. .0. .2

%e ..2. .1. .3. .3. .3. .2. .4. .1. .0. .0. .1. .1. .0. .2. .3. .1

%e ..2. .0. .4. .1. .0. .4. .2. .0. .1. .4. .2. .3. .1. .2. .3. .2

%Y Column 4 of A269619.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016